منابع مشابه
Practical Stability of Caputo Fractional Differential Equations by Lyapunov Functions
The practical stability of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov like function along the given fractional differential equation. Comparison results using this definition for scalar fractional differential equations are presented. Several ...
متن کاملFuzzy Lyapunov stability and exponential stability in control systems
Fuzzy control systems have had various applications in a wide range of science and engineering in recent years. Since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). Conceptually, there are two types of stability for control systems: Lyapunov stability (a special case ...
متن کاملStability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions
We study stability and stabilizability properties of systems with discontinuous righthand side (with solutions intended in Filippov’s sense) by means of locally Lipschitz continuous and regular Lyapunov functions. The stability result is obtained in the more general context of differential inclusions. Concerning stabilizability, we focus on systems affine with respect to the input: we give some...
متن کاملStructured and Simultaneous Lyapunov Functions for System Stability Problems
It is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of ẋ = Ax for some appropriate A. The existence of such a Lyapunov function can be determined by solving a convex program. We present several numerical methods for these optimization problems. A simple num...
متن کاملSOS-Convex Lyapunov Functions and Stability of Difference Inclusions
We introduce the concept of sos-convex Lyapunov functions for stability analysis of both linear and nonlinear difference inclusions (also known as discrete-time switched systems). These are polynomial Lyapunov functions that have an algebraic certificate of convexity and that can be efficiently found via semidefinite programming. We prove that sos-convex Lyapunov functions are universal (i.e., ...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1980
ISSN: 0040-8735
DOI: 10.2748/tmj/1178229544